**Chlorophyll Fluorescence in vivo: A
Theory (Part II). **

**Calculation of phytoplankton primary
production.**

Photosynthesis of microalgae can be measured as
the rate of radioactive carbon assimilation (Steemann Nielsen, 1952) or as an
increase in the concentration of soluble oxygen in a sample (Williams, 1982;
Langdon, 1984). These methods are rather labor-consuming, and their application
involves numerous artifacts due to prolonged isolation of phytoplankton in
bottles (Eppley, 1980), difference between net and gross photosynthesis (Bender
et al., 1987), and metal toxicity (Fitzwater et al., 1982). The application of
chlorophyll fluorescence methods avoids these problems and allows gross
photosynthesis of microalgae to be continuously measured in real time without
affecting their physiological state (Kolber et al., 1990; Green et al., 1992).
The relationship between chlorophyll a (*Chl _{a}*) fluorescence
and photosynthesis is described in a number of biophysical models of the
primary processes of photosynthesis (Weis and Berry, 1987; Genty et al.,1989;
Kiefer and Reynolds, 1992).

The model of carbon assimilation *V _{c}*
(mM C m

According this assumption the photosynthesis
rate is equal to:

*V _{c}*(I) = a

where I is the underwater radiation (mE m^{-2} s^{-1}).

The value of f(I) is proportional to the relative number of functionally active (¦), open (q_{P}) reaction centers PS II in algal cells, to the
efficiency of photochemical conversion of light energy in open reaction centers
(fRC, mM
electron mE^{-1}), and to the efficiency of CO_{2} reduction by electrons
from PS II (fe, mM C
(mM electron)^{-1}):

*V _{c}*(I) = (a

**Assessment of ****¦****, ****f**_{RC}** and ****f**** _{e}**:

The photochemical efficiency of open reaction
center of PS II can be determined from the ratio of fluorescence parameters: fRC =(*F _{v}*/

It was shown that the decrease in the *F _{v}*/

Thus, parameters fRC and ¦ are
proportional to the relative yield of variable fluorescence of chlorophyll in
microalgae adapted to natural radiation, so we assume:

¦*fRC=*F _{v}*/

** **

The value of fe was estimated from the following
considerations. To reduce one molecule of CO_{2}, 4 electrons should be
transferred from PS II , so, theoretical fe may be as high as 0.25, however, a fraction of
electron flow is used for nitrate and sulfate reduction (Dubinsky et al., 1986;
Laws, 1991), for cyclic electron transport around PS I (Slovacek et al., 1980;
Myers, 1987) and PS II (Falkowski et al., 1986a), as well as for O_{2}
reduction (Chemeris, 96). This parameter couldn't be measured by fluorescence
methods. Comparison of fe with the maximum quantum yield of carbon fixation allows to assume that
fe is approximately constant (Kiefer et al.,
1989; Morel, 1991) and is not over 0,16 for natural phytoplankton (Bannister
and Wiedmann, 1984). Thus, we assume that fe =0,16.

** **

**Determination of a _{PSP}**

** **

The intensity of fluorescence *F _{0 }*of
algae with open reaction centers (dark adapted) can be found from the equation:

*F _{0}* = G * I

where I_{fl} is the integral intensity of
exciting flash (in fluorometer PrimProd I_{fl}(l) is nearly uniformly distributed over spectral range 400-550 nm), a
constant; (a_{PSP})_{fl} is the coefficient of fluorescence
exciting flash absorption by PSP of PS II in algal suspension, averaged over
spectral range 400-550 nm; fFo is the quantum yield of fluorescence in cells with open RC; G is a
coefficient defined by geometric characteristics and sensitivity of the
fluorescence light sensor, a constant.

Taking into account that (G * I_{fl})^{-1} = const, the coefficient of underwater
radiation absorption by PSP of PS II of microalgae can be related to
fluorescence intensity as follows:

a_{PSP}
= const * fFo^{-1} * E * *F _{0}* = k(fFo, E) *

where E = a_{PSP}/(a_{PSP})_{fl}
= function (depth); k is a proportionality coefficient, which equals E/fFo.

We showed that E vary from 0,7 to 0,9 in the
water surface but is close to 1 in the depth 5 m and deeper. As was shown the
parameter fFo is a constant for natural phytoplankton
(Ostrowska et al*.*, 2000 a,b). Thus we assume parameter k(fFo, E) as a constant.

Value of parameter k can be obtained by
calibrating *Fo* against the coefficient of fluorescence exciting flash*
*absorption by microalgal cells in suspension a_{fl} (m^{-1})
taken at a natural concentration (*Chl _{a}*=0.1-10 mg m

Fig. 1. Dependences Fo *vs.*
a_{fl} for
diatomic *Th.
weissflogii* (square), green *Ch. vulgaris* (circle)
and yellow-green *N. salina* (triangle) algae.

**Determination of parameters q _{p} **

** **

It is known that photochemical conversion of
light energy in PS II takes place only in open reaction centers. The relative
concentration of open centers q_{p} can be found from the model of
light dependent transition of reaction centers between the open (with oxidized
Qa) and closed (with reduced Qa) states.

[Qa] [Qa^{-}][Qa] (6)

where *a*_{RC} - coefficient of
light absorption by antennas of single reaction center; K -
constant of Qa

oxidation rate (limiting reaction).

Making next replacements: [Qa]=q_{P}*[RC],
[Qa^{-}]=(1-q_{P})*[RC]

equation of reaction for q_{p} can be written: q_{p}(I)=K/(a_{RC}I*f_{RC}+K)

Replacing relation K/(a_{RC}*f_{RC}) by parameter I_{1/2} we derive hyperbolic dependence:

q_{p}(I) = I_{1/2}/(I+I_{1/2}) (7)

where I_{1/2} is light intensity, at which
half of the RC are in closed state.

Value of I_{1/2} can be found with accuracy
assigned by variations of parameter E which increases error of measurements in
the upper water (0-5 m). I_{1/2} is estimated from light dependence of
fluorescence obtained by pump-and-probe method (see Fig. 2).

Fig. 2. Estimation of I_{1/2}
from dependence of fluorescence yield on pump flash intensity.

**Assessment of phytoplankton photosynthesis rate
per hour**

By substituting 3, 5, 7, in 2 and introducing
the coefficient 6.9 = 12*10^{-3}
(mgC (mM C)^{-1}) *
3600 (s h^{-1}) * fe, the equation for vertical profile of algae
photosynthesis rate (mgC m^{-3} h^{-1}) can be written as
follows:

*V _{c}*(

where *z* is depth (m); k is constant for the
concrete fluorometer; I_{1/2} is measured in one or two water horizons.
Parameters of fluorescence and underwater radiation are estimated with minimal
frequency one measurement per meter of depth.

** **